PHAX: Physical Characteristics Aware Ex-Situ Training Framework for Inverter-Based Memristive Neuromorphic Circuits

In this paper, we propose a training framework for an inverter-based memristive neuromorphic hardware. The framework, which is called PHAX, is a physical characteristics aware one relying on an <italic>ex-situ</italic> training approach. The considered neuromorphic circuit is highly energy efficient hybrid CMOS-memristive implementation of neuromorphic circuits. To solve the problem of high sensitivity of the training to the mismatches between the high-level mathematical modeling of the neurons and the corresponding physical characteristics, an approach for analytical yet accurate modeling of the memristive crossbar and neuron circuits is suggested. The approach, which is based on SPICE simulations, models the inverter-based neurons using a hyperbolic tangent function. To increase the training efficacy, the backpropagation training algorithm is modified by considering some constraints based on the physical characteristics of the memristive circuit. This modification along with the accurate back-annotation of the physical characteristics considerably improve the effectiveness of the <italic>ex-situ</italic> training method of the neuromorphic circuit. The results of this paper show an average reduction of <inline-formula> <tex-math notation="LaTeX">$1805{\times }$ </tex-math></inline-formula> in the training runtime compared to that of the <italic>in-situ</italic> training approach. Furthermore, the results of applying the approach on the kernels of some applications such as image recognition, image processing, and financial analysis reveal that the designed neuromorphic circuits provide an average power saving (speed up) of <inline-formula> <tex-math notation="LaTeX">$1478{\times }$ </tex-math></inline-formula> (<inline-formula> <tex-math notation="LaTeX">$5.2{\times }$ </tex-math></inline-formula>) over the ASIC implementation in a 90-nm CMOS technology.